Chemical sensors based on plasmon resonance in graphene

ABSTRACT

Techniques for forming nanoribbon or bulk graphene-based SPR sensors are provided. In one aspect, a method of forming a graphene-based SPR sensor is provided which includes the steps of: depositing graphene onto a substrate, wherein the substrate comprises a dielectric layer on a conductive layer, and wherein the graphene is deposited onto the dielectric layer; and patterning the graphene into multiple, evenly spaced graphene strips, wherein each of the graphene strips has a width of from about 50 nanometers to about 5 micrometers, and ranges therebetween, and wherein the graphene strips are separated from one another by a distance of from about 5 nanometers to about 50 micrometers, and ranges therebetween. Alternatively, bulk graphene may be employed and the dielectric layer is used to form periodic regions of differing permittivity. A testing apparatus and method of analyzing a sample using the present SPR sensors are also provided.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application is a divisional of U.S. application Ser. No. 14/313,456filed on Jun. 24, 2014, the contents of which are incorporated byreference herein.

FIELD OF THE INVENTION

The present invention relates to surface plasmon resonance (SPR)sensors, and more particularly, to techniques for forming nanoribbon orbulk graphene-based SPR sensors and use thereof for analyzing chemicaland biological samples.

BACKGROUND OF THE INVENTION

Surface plasmon resonance (SPR) sensing has been demonstrated to be anexceedingly powerful and quantitative probe of the interactions of avariety of chemical and biological processes. SPR sensing provides ameans not only for identifying chemical and biological interactions andquantifying their kinetic and energetic properties, but also foremploying these interactions as very sensitive chemical and biologicaldetectors. Conventional SPR sensing is performed using plasmonsgenerated at a metal/dielectric interface, with the metal commonly beinggold. See, for example, J. Homola et al., “Surface Plasmon ResonanceSensors: Review,” Sensors and Actuators B: Chemical 54, 3 (January1999).

Conventional metal-based plasmonic materials, however, have certainnotable limitations. They are designed to operate at predeterminedresonance frequencies, which cannot be substantially tuned. Furthermore,the use of metals requires three dimensional design ofplasmon-generating structures, and the plasmon field confinement andpropagation length are determined by the metal conductivity. It is inthese ways that conventional metal-based plasmonic materials arelimited.

Thus, improved plasmonic materials for SPR sensing would be desirable.

SUMMARY OF THE INVENTION

The present invention provides techniques for forming nanoribbon or bulkgraphene-based surface plasmon resonance (SPR) sensors and use thereoffor analyzing chemical and biological samples. In one aspect of theinvention, a method of forming a graphene-based SPR sensor is providedwhich includes the steps of: depositing graphene onto a substrate,wherein the substrate comprises a dielectric layer on a conductivelayer, and wherein the graphene is deposited onto the dielectric layer;and patterning the graphene into multiple, evenly spaced graphenestrips, wherein each of the graphene strips has a width of from about 50nanometers to about 5 micrometers, and ranges therebetween, and whereinthe graphene strips are separated from one another by a distance of fromabout 5 nanometers to about 50 micrometers, and ranges therebetween.

In another aspect of the invention, another method of forming agraphene-based SPR sensor is provided which includes the steps of:depositing a dielectric layer on a conductive layer; patterning trenchesat regular intervals in the dielectric layer to transform the dielectriclayer into a corrugated surface having a series of grooves and ridges,wherein the grooves are formed by the trenches and the ridges are formedby the dielectric layer remaining between the trenches; and depositingbulk graphene onto the corrugate surface of the dielectric layer,wherein the corrugated surface of the dielectric layer provides periodicregions of differing permittivity beneath the bulk graphene including i)first regions having a first permittivity to light and ii) secondregions having a second permittivity to light.

In a further aspect of the invention, a testing apparatus is provided.The testing apparatus includes a graphene-based SPR sensor having aconductive layer, a dielectric layer on the conductive layer, andgraphene on a side of the dielectric layer opposite the conductivelayer; a light source adjacent to a first side of the graphene-based SPRsensor proximal to the graphene; and a detector adjacent to a secondside of the graphene-based SPR sensor proximal to the conductive layer.The graphene may include multiple, evenly spaced graphene strips,wherein each of the graphene strips has a width of from about 50nanometers to about 5 micrometers, and ranges therebetween, and whereinthe graphene strips are separated from one another by a distance of fromabout 5 nanometers to about 50 micrometers, and ranges therebetween. Thedielectric layer may have trenches patterned at regular intervalstherein such that the dielectric layer includes a corrugated surfacehaving a series of grooves and ridges, wherein the grooves are formed bythe trenches and the ridges are formed by the dielectric layer remainingbetween the trenches, and wherein the corrugated surface of thedielectric layer provides periodic regions of differing permittivitybeneath the bulk graphene including i) first regions having a firstpermittivity to light and ii) second regions having a secondpermittivity to light.

In yet another aspect of the invention, a method of analyzing a sampleusing a graphene-based SPR sensor is provided which includes the stepsof: depositing the sample on the graphene-based SPR sensor, wherein thegraphene-based SPR sensor includes a conductive layer, a dielectriclayer on the conductive layer, and graphene on a side of the dielectriclayer opposite the conductive layer, and wherein the sample is depositedonto the graphene; passing light through the sample and thegraphene-based SPR sensor, wherein the light induces a plasmon resonancein the graphene, and wherein, by way of an interaction between theplasmon resonance in the graphene and vibrational dipole moments in thesample, an intensity of the light is changed as it passes through thegraphene-based SPR sensor; and detecting the intensity of the light thathas passed through the sample and the graphene-based SPR sensor, whereinthe intensity of light detected represents molecular properties of thesample.

A more complete understanding of the present invention, as well asfurther features and advantages of the present invention, will beobtained by reference to the following detailed description anddrawings.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a cross-sectional diagram illustrating a starting structurefor forming a graphene-based surface plasmon resonance (SPR) sensorusing graphene nanoribbons, the structure including a graphene layer ona side of a dielectric layer opposite a conductive layer according to anembodiment of the present invention;

FIG. 2 is a cross-sectional diagram illustrating an etch mask havingbeen patterned on the graphene layer according to an embodiment of thepresent invention;

FIG. 3 is a cross-sectional diagram illustrating the etch mask havingbeen used to pattern the graphene layer into the graphene nanoribbonsaccording to an embodiment of the present invention;

FIG. 4 is a cross-sectional diagram illustrating the etch mask havingbeen removed following patterning of the nanoribbons according to anembodiment of the present invention;

FIG. 5 is a cross-sectional diagram illustrating an optional coatinghaving been deposited onto the substrate covering and protecting thegraphene nanoribbons according to an embodiment of the presentinvention;

FIG. 6 is a cross-sectional diagram illustrating a starting structurefor an alternative process for forming a graphene-based SPR sensor usingbulk graphene, the structure including a dielectric layer opposite aconductive layer according to an embodiment of the present invention;

FIG. 7 is a cross-sectional diagram which, following from FIG. 6,illustrates an etch mask having been formed on the dielectric layeraccording to an embodiment of the present invention;

FIG. 8 is a cross-sectional diagram which, following from FIG. 7,illustrates the etch mask having been used to pattern the insulatingdielectric layer according to an embodiment of the present invention;

FIG. 9 is a cross-sectional diagram which, following from FIG. 8,illustrates the etch mask having been removed revealing that thepatterned insulating dielectric layer has a corrugated surfaceconsisting of ridges and grooves according to an embodiment of thepresent invention;

FIG. 10 is a cross-sectional diagram which, following from FIG. 9,illustrates graphene having been deposited onto the substrate accordingto an embodiment of the present invention;

FIG. 11 is a cross-sectional diagram which, following from FIG. 10,illustrates an optional coating having been deposited onto the sensor tocover and protect the graphene according to an embodiment of the presentinvention;

FIG. 12 is a cross-sectional diagram which, following from FIG. 7,illustrates in an alternative bulk graphene-based embodiment the etchmask having been used to pattern trenches in the insulating dielectriclayer that extend down to the surface of the conductive layer accordingto an embodiment of the present invention;

FIG. 13 is a cross-sectional diagram which, following from FIG. 12,illustrates a second (different permittivity) material having beendeposited onto the substrate, overfilling each of the trenches accordingto an embodiment of the present invention;

FIG. 14 is a cross-sectional diagram which, following from FIG. 13,illustrates the second material having been polished down to the surfaceof the insulating dielectric layer according to an embodiment of thepresent invention;

FIG. 15 is a cross-sectional diagram which, following from FIG. 14,illustrates graphene having been deposited onto the substrate accordingto an embodiment of the present invention;

FIG. 16 is a cross-sectional diagram which, following from FIG. 15,illustrates an optional coating having been deposited onto the sensor tocover and protect the graphene according to an embodiment of the presentinvention;

FIG. 17 is a cross-sectional diagram illustrating a sample having beendeposited onto the present SPR sensor according to an embodiment of thepresent invention;

FIG. 18 is a diagram which, following from FIG. 17, illustrates thepresent SPR sensor being used to analyze the sample according to anembodiment of the present invention;

FIG. 19 is a graph illustrating an effect graphene nanoribbons width hason plasma resonance according to an embodiment of the present invention;and

FIG. 20 is a diagram which, following from FIG. 17, illustrates analternative (reflection measurement-based) use of the present SPR sensorto analyze the sample according to an embodiment of the presentinvention.

DETAILED DESCRIPTION OF PREFERRED EMBODIMENTS

Provided herein are graphene-based plasmonic materials and chemicalsensors based on plasmon resonance in graphene (i.e., wherein grapheneis the surface plasmon active material in the sensor). Graphene plasmonactive materials do not suffer from the above-described drawbackscommonly encountered with conventional metal-based plasmonic materialssuch as gold and silver.

For instance, several factors make graphene a unique platform forplasmon-enhanced infrared spectroscopy: 1) graphene has atwo-dimensional lattice structure which allows for a very high plasmonconfinement field that cannot be achieved with metal-based plasmons,which promises high sensitivity; 2) the charge concentration of graphene(i.e., the number of majority carriers per unit volume) can be modulatedthrough chemical doping or the field-effect (wherein tuning in thismanner is not possible with metal plasmonic structures); 3) the chargeconcentration profile can be patterned in graphene using standardtechniques; and 4) the excitation and coupling to surface plasmons inthe resulting structure can be easily achieved. The high carriermobility and conductivity that are facilitated by the lattice structureof graphene allows for high plasmon field confinement and large plasmonpropagation lengths as compared to more conventional gold surfaces ofsimilar thickness. Also, modulation of the charge concentration allowsfor tuning of surface plasmon energies in graphene, something thatcannot be achieved in gold or any other metal. Furthermore, plasmonresonances in graphene can be generated and coupled directly to light byphysical confinement of the charge oscillations or by attaching grapheneto a dielectric grating. Physical confinement can be achieved by routineoxygen plasma etching, and dielectric grating substrates can beengineered using conventional complementary metal-oxide semiconductor(CMOS) fabrication techniques. See below. Lastly, the plasmon resonancefrequency of graphene is in the infrared regime, where most chemicalshave their characteristic vibration signals. This makes graphene anatural fit for chemical sensing applications. Thus, it is clear thatsurface plasmon generation from graphene has characteristics that otherplasmon-generating systems lack.

The present techniques are now described in detail by way of referenceto FIGS. 1-20. Specifically, an exemplary process for forminggraphene-based surface plasmon resonance (SPR) sensors using graphenenanoribbons is provided in FIGS. 1-5. Alternative exemplary processesfor forming SPR sensors using bulk graphene are provided in FIGS. 6-11(employing a corrugated surface) and FIGS. 12-16 (employing a planarsurface with periodic regions of different permittivity). Methods ofusing the present graphene-based SPR sensors for analyzing a sample arethen provided in FIGS. 17-18, and 20.

Referring to FIGS. 1-5, a first exemplary method for forming the presentgraphene-based SPR sensors is provided. In this example, the graphene ispatterned as nanoribbons. As shown in FIG. 1, the process begins with alayer of graphene 102 being deposited on a substrate 104. The substrate104 preferably includes a (electrically) conductive layer 104 a (whichwill serve as a back gate of the sensor—see below) and an insulatingdielectric layer 104 b, such that the insulating dielectric layer 104 bis deposited on the conductive layer 104 a, and the graphene 102 isdeposited on a side of the insulating dielectric layer 104 b oppositethe conductive layer 104 a. See FIG. 1.

A suitable (electrically conductive) material for forming conductivelayer 104 a includes, but is not limited to, intrinsic silicon.Embodiments of the present techniques involve analyzing a sample bypassing light through the sample and the sensor (a transmissionmeasurement). In that case, intrinsic silicon is ideal since it istransparent in the correct spectral range and can also be used as anelectrostatic gate electrode. Alternatively, conventional gate metalsmight be employed. For example, one or more of tantalum, titanium,platinum and/or tungsten may be used in forming the conductive layer 104a. However, since these gate metals are not transparent to light,configurations of the present sensors employing a metal back gate wouldneed to be read via a reflection measurement. Any insulating dielectricwould be a suitable material for forming insulating dielectric layer 104b. Examples include, but are not limited to, gate dielectrics such assilicon dioxide and aluminum oxide, and high-κ dielectrics such ashafnium oxide or lanthanum oxide.

According to an exemplary embodiment, the insulating dielectric layer104 b has a thickness T_(Dielectric1) of from about 1 nanometer (nm) toabout 5 nm, and ranges therebetween. See FIG. 1. By contrast, in thebulk graphene-based fabrication process flows presented below, a thickerstarting dielectric layer is desirable so as to permit the dielectric tobe partially etched away to form a corrugated surface. It would beapparent to one of skill in the art how to control the thickness of adielectric layer during deposition onto a given substrate. By way ofexample only, a suitable process for depositing the insulatingdielectric layer 104 b on the conductive layer 104 a includes, but isnot limited to, chemical vapor deposition (CVD).

Graphene is a material that consists of one atom thick sheets of carbon.According to an exemplary embodiment, graphene layer 102 actuallyincludes from 1 (i.e., a graphene monolayer) up to a stack of about 5graphene sheets, and ranges therebetween. By way of example only,graphene layer 102 may be deposited (or grown) on the substrate 104using any suitable deposition process including, but not limited to,mechanical exfoliation, epitaxial growth, a transfer process and CVD.While exfoliation is ideal for obtaining high quality (i.e., low amountof structural defects), there are tradeoffs. For instance, thedimensions (size, thickness, etc.) of the sample are hard to controlwith exfoliation. Thus, processes such as CVD of graphene can be aviable alternative. A CVD process for graphene deposition is described,for example, in Mattevi et al., “A review of chemical vapour depositionof graphene on copper,” J. Mater. Chem., 2011, 21, 3324-3334 (firstpublished November 2010) (hereinafter “Mattevi”), the contents of whichare incorporated by reference as if fully set forth herein.Alternatively, graphene sheets grown on another substrate (e.g., by CVDon a copper substrate—see Mattevi) can be subsequently transferred tothe substrate 104. See, for example, Ko et al., “Simple method totransfer graphene from metallic catalytic substrates to flexiblesurfaces without chemical etching,” Journal of Physics: ConferenceSeries, Vol. 433, Issue 1 (April 2013) 012002 (hereinafter “Ko”), thecontents of which are incorporated by reference as if fully set forthherein.

Optionally, the graphene may be doped. Doping of the graphene can(optionally) be performed at a number of different points in theprocess. For instance, the graphene can be doped before, after, orduring (i.e., in situ doping) being transferred or deposited onto thesubstrate. Suitable dopants for the graphene include, but are notlimited to, polyethylene imine (PEI) (n-type) and diazonium salts(p-type). See, for example, Farmer et al., “Behavior of a ChemicallyDoped Graphene Junction,” Applied Physics Letters 94, 213106 (May 2009),the contents of which are incorporated by reference as if fully setforth herein. Doping of the graphene modifies the carrier concentration,and hence plasmon resonance, in the graphene. Accordingly, doping may beused instead of, or in addition to, back-gating the sensor. It isnotable however that being able to back gate the sensor is advantageousto permit in situ adjustments to be made. Thus a back gate (i.e.,conductive layer) is included in each of the embodiments describedherein with the understanding that graphene doping alone may be employed(in which case a back gate would not be needed). The effects ofback-gating doped graphene to alter the carrier concentration aredescribed in detail below.

As will be described in detail below, in this exemplary embodiment, thegraphene 102 is divided into multiple nanoribbons using, for example, alithography and etching process. The term “nanoribbon” as used hereingenerally refers to strips of graphene each having a width w of fromabout 50 nm to about 5 micrometers, and ranges therebetween. See below.Since the graphene nanoribbons are to be patterned from graphene layer102, each of the nanoribbons likewise will consist of from about 1 (amonolayer) up to a stack of about 5 sheets of graphene and rangestherebetween. As will be described in detail below, the width of thenanoribbons is one factor (e.g., along with the charge density) thataffects, and thus can be used to control, the plasmon resonance. Anexample showing the effect of varying nanoribbon width is shownillustrated in FIG. 19, described below.

To form the graphene 102 into nanoribbons, an etch mask 202 is firstpatterned on the graphene 102. See FIG. 2. Specifically, to form theetch mask 202, a resist material is first deposited onto a side ofgraphene layer 102 opposite the substrate 104. Standard lithography andetching techniques are then employed to pattern the resist material intothe etch mask 202. By way of example only, a suitable resist materialincludes, but is not limited to, polymethyl methacrylate (PMMA). PMMAcan be spin-coated onto the graphene layer 102 and patterned, e.g.,using e-beam lithography. A pre bake (prior to patterning) of a PMMAresist is preferably employed, e.g., at a temperature of from about 170degrees Celsius (° C.) to about 190° C. and ranges therebetween, for aduration of from about 1 minute to about 30 minutes and rangestherebetween. Following patterning, an optional postbake and hardeningof the PMMA may be conducted, e.g., at a temperature of from about 90°C. to about 110° C. and ranges therebetween, for a duration of fromabout 1 minute to about 30 minutes and ranges therebetween.

Next, as shown illustrated in FIG. 3, the etch mask 202 is used topattern the graphene layer 202 into multiple graphene nanoribbons 302.According to an exemplary embodiment, this etching step is carried outusing a dry etching process, such as an oxygen reactive ion etching(RIE) process, which is used to etch away the graphene not covered bythe etch mask 202 (i.e., the graphene is etched through the etch mask202).

Following patterning of the nanoribbons 302, the etch mask 202 isremoved. See FIG. 4. By way of example only, when the etch mask 202 isformed from PMMA, it can be dissolved in acetone. As highlighted above,the width of the resulting nanoribbons 302 affects, and thus can be usedto control, the plasmon resonance. In general, as the dimension (e.g.,width w—see below) of the graphene structure decreases the plasmonresonance frequency increases, and vice versa. While there may bedifferent quantitative relations for different structure shapes, this isthe general trend. It is also notable that the ‘critical dimension’ ofthe graphene with respect to plasmon resonance is the dimension that isparallel to the polarization of the incident light. For example, withnanoribbons, plasmons are excited in graphene when the lightpolarization is parallel to the width (small dimension) of thenanoribbon. Plasmons are not excited when the light polarization isparallel to the length (large dimension) of the nanoribbon.

By way of example only, each of the nanoribbons 302 patterned in thisstep has a width w (see FIG. 4) of from about 50 nm to about 5micrometers, and ranges therebetween, and consists of from 1 (amonolayer) to a stack of up to about 5 sheets of graphene and rangestherebetween. As shown in FIG. 4, the nanoribbons 302 patterned in thismanner form multiple, evenly spaced strips (each having a width w) onthe surface of the insulating dielectric layer 104 b. This periodic(i.e., occurring at regular intervals), repeating pattern of nanoribbonstrips will permit coupling of incident light to the plasmon resonancein the graphene. According to an exemplary embodiment, the strips (i.e.,nanoribbons 302) are separated from each other by a distance x.Specifically, each strip (i.e., nanoribbon 302) is separated from anadjacent nanoribbon(s) 302 to either side by a distance x, wherein x isfrom about 5 nm to about 50 micrometers (μm) and ranges therebetween.

During operation of the sensor, the patterned graphene (i.e.,nanoribbons 302) will permit coupling of incident light with thegraphene plasmons. By comparison, in the case of the bulk graphene-basedsensors described below, this coupling occurs via the formation ofregions of different dielectric permittivity. In either the case ofpatterned graphene nanoribbons or bulk graphene over regions ofdifferent dielectric permittivity, coupling of incident light with thegraphene plasmons occurs as a result of a general grating effect that isubiquitous in plasmonics. In general, the grating (periodic regions ofdiffering permittivity) is a coupler, matching the surface-parallelcomponent of the light wavevector with the plasmon wavevector. Theamount of matching depends on the period of the grating and wavelengthof the light. The underlying plasmon excitation mechanism is the same inboth cases since in both cases there is a grating, i.e., regions ofdiffering periodic permittivity.

Finally, as shown in FIG. 5 an optional coating 502 can be depositedonto the substrate 104 covering the nanoribbons 302 to protect thegraphene nanoribbons 302 during use of the device. According to anexemplary embodiment, this optional protective coating 502 is formedfrom a transparent dielectric material, such as silicon dioxide. Whenpresent, the optional protective coating is thin enough to allow theplasmon field to extend through it, maintaining plasmon-induced signalmodification. By way of example only, the protective coating has athickness T_(Coating) of from about 1 nm to about 5 nm and rangestherebetween, e.g., wherein T_(Coating) is measured at a thickest partof the coating 502. See FIG. 5.

As will be described in detail below, when the present graphene-basedSPR sensors are used to analyze a sample, the sample is deposited onto(the graphene side of) the sensor and light may be passed (from a lightsource proximal to the graphene side of the sensor) through both thesample and the sensor and is picked up by a detector (proximal to thesubstrate side of the sensor). In that case, all components of thesensor should be substantially transparent to the frequency range of thelight being used. The above-described materials meet those criteria.While the insulating dielectrics may absorb some small amount of lightin certain spectral ranges, this will not have an impact on thereadings. More at issue is the back gate material (e.g., conductivelayer 104 a). Normal metals might not work for a transmissionmeasurement (but could work for a reflection measurement). Fortransmission, the back gate material can be intrinsic silicon. Intrinsicsilicon is transparent in the correct spectral range and can also beused as an electrostatic gate electrode.

The present graphene-based SPR sensors may also be produced using bulkgraphene. The use of bulk graphene eliminates the (above-described)steps needed to pattern the graphene nanoribbons, thus simplifying theprocess. It is notable that while a simplified process is easier toimplement and lowers overall production costs, one tradeoff of bulkgraphene versus nanoribbons is a loss in the ability to tune the plasmonresonance by graphene patterning (i.e., the width of the nanoribbons canbe tailored to tune the plasmon resonance—see above).

A first exemplary process for forming the present SPR sensors using bulkgraphene is now provided by way of reference to FIGS. 6-11. As will bedescribed in detail below, the bulk graphene-based embodiments, employpatterning a surface of the substrate onto which the graphene isdeposited. The patterned substrate surface provides the sensor withperiodic regions of differing (light) permittivity provided by portionsof the insulating dielectric substrate and a second material,respectively. In the exemplary embodiment illustrated in FIGS. 6-11, thesecond material is air, and in another bulk graphene-based embodimentillustrated in FIGS. 12-16, the second material is a dielectric with adifferent permittivity from the substrate dielectric.

Referring now to FIG. 6, an exemplary process for forming the presentSPR sensors using bulk graphene begins with a substrate 602 whichincludes a (electrically) conductive layer 602 a (which will serve as aback gate of the sensor—see below) and an insulating dielectric layer602 b deposited on the conductive layer 602 a. By comparison with theembodiment illustrated in FIGS. 1-5, described above, the insulatingdielectric layer 602 b initially needs to be thicker to permit furtherprocessing of the layer, e.g., so as to form a corrugated surface. Seebelow. Thus, according to an exemplary embodiment, the insulatingdielectric layer 602 b has a thickness T_(Dielectric2) of from about 4nm to about 300 nm and ranges therebetween. See FIG. 6. It would beapparent to one of skill in the art how to control the thickness of adielectric layer during deposition onto a given substrate. By way ofexample only, a suitable process for depositing the insulatingdielectric layer 602 b on the conductive layer 602 a includes, but isnot limited to, CVD.

As above, a suitable (electrically conductive) material for formingconductive layer 602 a includes, but is not limited to, intrinsicsilicon. Embodiments of the present techniques involve analyzing asample by passing light through the sample and the sensor (atransmission measurement). In that case, intrinsic silicon is idealsince it is transparent in the correct spectral range and can also beused as an electrostatic gate electrode. Alternatively, conventionalgate metals might be employed. For example, one or more of tantalum,titanium, platinum and/or tungsten may be used in forming the conductivelayer 602 a. However, since these gate metals are not transparent tolight, configurations of the present sensors employing a metal back gatewould need to be read via a reflection measurement. Any insulatingdielectric would be a suitable material for forming insulatingdielectric layer 602 b. Examples include, but are not limited to, gatedielectrics such as silicon dioxide, aluminum oxide, and high-κdielectrics such as hafnium oxide or lanthanum oxide.

Next, the insulating dielectric layer 602 b of substrate 602 ispatterned to form a corrugated surface. Specifically, portions of theinsulating dielectric layer 602 b will be etched away resulting in theformation of a grated surface of the insulating dielectric layer 602 b(opposite the conductive layer 602 a) onto which the bulk graphene isdeposited.

As shown in FIG. 7, the process of patterning of the insulatingdielectric layer 602 b begins with the formation of an etch mask 702 onthe insulating dielectric layer 602 b. Specifically, to form the etchmask 702, a resist material is first deposited onto a side of theinsulating dielectric layer 602 b opposite the conductive layer 602 a.Standard lithography and etching techniques are then employed to patternthe resist material into the etch mask 702. By way of example only, asuitable resist material includes, but is not limited to, PMMA. Asdescribed in detail above, PMMA can be spin-coated onto the substrateand patterned, e.g., using e-beam lithography. As described above, a prebake and an optional postbake of the PMMA resist can be performed.Exemplary parameters (i.e., temperature and duration) of these bakingsteps were provided above.

The etch mask 702 is then used to pattern the insulating dielectriclayer 602 b. See FIG. 8. Specifically, the etch mask 702 is used topattern trenches at regular intervals in the surface of insulatingdielectric layer 602 b to transform the surface of insulating dielectriclayer 602 b into a grated or corrugated surface having a series ofgrooves (formed by the trenches 802) and ridges (formed by the portionsof the insulating dielectric layer 602 b remaining in between thetrenches 802). See FIG. 8. As shown in FIG. 8 it is desirable to timethe etch so as not to etch completely through the insulating dielectriclayer 602 b (i.e., following the etch, a portion of the insulatingdielectric layer 602 b preferably remains at the bottom of each of thetrenches 802). Thus the trenches 802 extend only partway through thedielectric layer 602 b. By way of example only, a RIE process may beused to remove portions of the insulating dielectric layer 602 b notcovered by the etch mask 702. The RIE may be endpointed prior tocompletely etching through the insulating dielectric layer 602 b. Areason for leaving a portion of the insulating dielectric layer 602 b atthe bottom of each of the trenches 802 is to prevent the graphene, whichmay potentially bend into the trench during operation, from touching theexposed conductive material and “shorting” the device. According to anexemplary embodiment, this portion of the insulating dielectric layerleft at the bottom of the trenches has a minimum thickness of about 5nm, e.g., from about 5 nm to about 20 nm and ranges therebetween.Further, the deeper the trenches 802, the better, because the dielectricmismatch will be enhanced. By way of example only, each of the trenches802 preferably has a depth d of from about 4 nm to about 300 nm andranges therebetween.

The goal here is to produce a dielectric surface (onto which graphenecan be deposited) that consists of regions of different (light)permittivity. In this example, the ridges in the insulating dielectriclayer 602 b surface serve as the first regions, wherein the insulatingdielectric layer 602 b has a first permittivity to light. The groovesformed by the trenches 802 in the insulating dielectric layer 602 bsurface serve as the second regions, wherein the air within the trenches802 has a second permittivity to light. See FIG. 9. This periodic (i.e.,occurring at regular intervals), repeating, alternating of regions ofdiffering permittivity will permit coupling of incident light to theplasmon resonance in the graphene. According to an exemplary embodiment,the first regions are separated from each other by a (first) distance X(measured as a distance from a center of one first region to a center ofanother, adjacent first region) and the second regions are separatedfrom each other by a (second) distance Y (measured as a distance from acenter of one second region to a center of another, adjacent secondregion), wherein X and Y each are from about 5 nm to about 20 nm andranges therebetween. As also shown in FIG. 9, following patterning ofthe trenches 802, the etch mask 702 may be removed. By way of exampleonly, when the etch mask 702 is formed from PMMA, it can be dissolved inacetone.

Following the dielectric etch (and etch mask removal), graphene 1002 isthen deposited onto the substrate. See FIG. 10. Specifically, as shownin FIG. 10, the graphene 1002 is deposited onto the now corrugatedsurface of the insulating dielectric layer 602 b (i.e., the side of theinsulating dielectric layer 602 b opposite the conductive layer 602 a).With this configuration, the graphene 1002 will cover both i) the firstregions (the ridges in the insulating dielectric layer 602 b) having thefirst permittivity to light and ii) the second regions (the groovesformed by the trenches in the insulating dielectric layer 602 b whichare filled with air) having the second permittivity to light. Couplingof incident light with graphene plasmons is thus allowed due to theperiodic permittivity of the surface. As described above, the periodicgrating (either via the patterned graphene nanoribbons or the regions ofdifferent dielectric permittivity) allows for matching of the lightwavevector and plasmon wavevector, and therefore coupling of theincident light with the plasmon.

As above, the graphene 1002 may be a layer having from 1 (i.e., agraphene monolayer) up to a stack of about 5 graphene sheets, and rangestherebetween. Suitable processes for depositing and/or growing graphenewere described above. However, in this case, the desired result is aplanar layer of graphene over the ridges and grooves in the surface ofthe insulating dielectric layer 602 b. Thus, a transfer process ispreferable, wherein a sheet(s) of the graphene are transferred to thecorrugated surface of the insulating dielectric layer 602 b over theridges and grooves. See FIG. 10. By way of example only, graphene sheetsgrown on another substrate (e.g., by CVD on a copper substrate—seeMattevi) can be subsequently transferred to the (corrugated) surface ofthe insulating dielectric layer 602 b. See, for example, Ko. In thiscase, the graphene 1002 is not patterned into ribbons, and thus canremain in its as deposited, bulk form.

As above, the graphene may optionally be doped to modify the carrierconcentration, and hence plasmon resonance, in the graphene. Suitabledopants include, but are not limited to, PEI (n-type) and diazoniumsalts (p-type). As described above, while doping may be used instead ofback-gating the sensor, having a back gate is advantageous to permit insitu adjustments to be made. Thus it may be desirable to have a backgate in combination with a doped graphene layer. The effects ofbackgating doped graphene to alter the carrier concentration aredescribed in detail below.

Finally, as shown in FIG. 11 an optional coating 1102 can be depositedonto the sensor covering the graphene layer 1002 to protect the grapheneduring use of the device. As provided above, this optional protectivecoating 1102 can be formed from a transparent dielectric material, suchas silicon dioxide, and should be thin enough to allow the plasmon fieldto extend through it, maintaining plasmon-induced signal modification.By way of example only, the protective coating has a thicknessT_(Coating) of from about 1 nm to about 5 nm and ranges therebetween.See FIG. 11.

While providing periodic regions of different permittivity using air(present in the trenches of the corrugated surface) as one of thematerials, there is a chance that electrostatic forces might cause thegraphene to bend into the grooves formed by the trenches. To preventthis distortion of the graphene from occurring, it is also possible toemploy a material (other than air) in the trenches having a differentpermittivity (to light). In the example illustrated in FIGS. 12-16, thismaterial is a different dielectric material from that used in thesubstrate which has a different permittivity to light. Like theembodiment illustrated in FIGS. 6-11, this process also employs bulkgraphene.

As with the other bulk graphene-based example illustrated in FIGS. 6-11,this exemplary embodiment also involves patterning the substratedielectric to form a corrugated surface thereon. Therefore, the firstfew steps of the two bulk graphene-based process flows are the same.Specifically, each begins with a thick insulating dielectric layer 602 bon a conductive layer 602 a. See FIG. 6, described above. An etch mask702 is then formed on a side of the insulating dielectric layer 602 bopposite the conductive layer 602 a. As described above, the etch mask702, e.g., via a RIE process, will be used to pattern the insulatingdielectric layer 602 b into a corrugated layer including ridges andgrooves.

It is at this point in the process flow where the two techniques differ.Thus, following from FIG. 7, FIG. 12 illustrates how in this case anetch is used to remove portions of the insulating dielectric layer 602 bnot covered by etch mask 702 down to the conductive layer 602 a,resulting in the formation of trenches 1202 that extend down to thesurface of the conductive layer 602 a. See FIG. 12. Specifically, sincethe trenches 1202 will be filled (e.g., with a different dielectricmaterial), then it is not necessary that any of the insulatingdielectric layer 602 b material remain in the trenches (compare, forexample, FIG. 12 with FIG. 8—described above).

As described above, the goal of etching the insulating dielectric layer602 b is to pattern trenches 1202 at regular intervals in the insulatingdielectric layer 602 b to transform the insulating dielectric layer 602b into a grated or corrugated layer having a series of grooves (formedby the trenches 1202) and ridges (formed by the portions of theinsulating dielectric layer 602 b remaining in between the trenches1202). See FIG. 12. In this case, however, the trenches 1202 preferablyextend completely through the insulating dielectric layer 602 b down tothe surface of the conductive layer 602 a. According to an exemplaryembodiment, a RIE process is used to pattern the insulating dielectriclayer 602 b through the etch mask 702. In this case, the conductivelayer 602 a can serve as an etch stop for the RIE. Following the trenchetch, the etch mask 702 can be removed. By way of example only, when theetch mask 702 is formed from PMMA, it can be dissolved in acetone.

The goal here is to produce a dielectric surface (onto which graphenecan be deposited) that consists of regions of different (light)permittivity. In this example, the ridges in the insulating dielectriclayer 602 b surface serve as the first regions, wherein the insulatingdielectric layer 602 b has a first permittivity to light. A secondmaterial which will be filled into the grooves formed by the trenches1202 in the insulating dielectric layer 602 b surface will serve as thesecond regions, wherein the second material has a second permittivity tolight. See FIG. 14, described below.

Specifically, after the etch mask 702 has been removed, the process forfilling the trenches 1202 with a second (different permittivity)material begins by blanket depositing the second material 1302 onto thesubstrate, overfilling each of the trenches 1202. See FIG. 13. By way ofexample only, the insulating dielectric layer 602 b can be silicondioxide (see above), and the second material 1302 can be aluminum oxideor hafnium oxide, or vice versa. Strictly speaking, all materials havedifferent permittivities because of their different elementalcompositions. Thus using two different dielectric materials fordielectric layer 602 b and material 1302 would result in differentpermittivities. However, it is desirable here to have the highestpermittivity mismatch possible. That will generate the strongest plasmonexcitation. Therefore, the combination of a high-κ material like hafniumoxide (κ=20) and silicon dioxide (κ=4) would be good. Even better is avacuum (κ=1) in combination with a high-κ dielectric, which can berealized in the embodiment where the trenches are left empty and coveredover with bulk graphene. See FIG. 10, described above.

In order to provide a flat surface onto which the graphene can bedeposited, the second material 1302 is then polished down to the surfaceof the insulating dielectric layer 602 b. As a result, a surface of thesecond material 1302 will be coplanar with a top surface of the ridgesin the insulating dielectric layer 602 b. See FIG. 14. According to anexemplary embodiment, the second material 1302 is polished usingchemical mechanical polishing (CMP). Depending on the selectivity of theCMP process, this polishing step will also serve to planarize the topsof the ridges, additionally insuring that a flat surface is provided forgraphene deposition.

As shown in FIG. 14, the result is the substrate having periodic regionsof different permittivity wherein the first regions (formed from theridges in the insulating dielectric layer 602 b) have a firstpermittivity to light, and the second regions (formed from the secondmaterial 1302 filled in the trenches) have a second permittivity tolight. This periodic (i.e., occurring at regular intervals), repeating,alternating of regions of differing permittivity will permit coupling ofincident light to the plasmon resonance in the graphene. According to anexemplary embodiment, the first regions are separated from each other bya (first) distance X′ (measured as a distance from a center of one firstregion to a center of another, adjacent first region) and the secondregions are separated from each other by a (second) distance Y′(measured as a distance from a center of one second region to a centerof another, adjacent second region), wherein X′ and Y′ each are fromabout 5 nm to about 20 nm and ranges therebetween.

Graphene 1502 is then deposited onto the substrate. See FIG. 15.Specifically, as shown in FIG. 15, the graphene 1502 is deposited ontothe surface of the substrate opposite the conductive layer 602 a nowhaving periodic regions of different permittivity from the alternatingmaterials of different permittivity on that surface (e.g., thealternating ridges in insulating dielectric layer 602 b and the secondmaterial 1302 in the trenches therebetween). Thus, with thisconfiguration, the graphene 1502 will cover both i) the first regions(the ridges in the insulating dielectric layer 602 b) having the firstpermittivity to light and ii) the second regions (the grooves formed bythe trenches in the insulating dielectric layer 602 b which are filledwith the second material 1302) having the second permittivity to light.Coupling of incident light with graphene plasmons is thus allowed due tothe periodic permittivity of the surface. As described above, theperiodic grating (either via the patterned graphene nanoribbons or theregions of different dielectric permittivity) allows for matching of thelight wavevector and plasmon wavevector, and therefore coupling of theincident light with the plasmon.

As above, the graphene 1502 may be a layer having from 1 (i.e., agraphene monolayer) up to a stack of about 5 graphene sheets, and rangestherebetween. Suitable processes for depositing and/or growing graphenewere described above. By comparison with the example provided in FIGS.6-11 above wherein the graphene is deposited over the empty grooves (andridges), here the grooves are filled with a second material (other thanair). Thus, a planar surface is present onto which the graphene can bedeposited. Accordingly, any of the above-described exemplary processesfor depositing (or growing) graphene on a surface which include, but arenot limited to, mechanical exfoliation, epitaxial growth, a transferprocess and CVD, may be employed. In this case, the graphene 1502 is notpatterned into ribbons, and thus can remain in its as deposited, bulkform.

Finally, as shown in FIG. 16 an optional coating 1602 can be depositedonto the sensor covering the graphene layer 1502 to protect the grapheneduring use of the device. As provided above, this optional protectivecoating 1602 can be formed from a transparent dielectric material, suchas silicon dioxide, and should be thin enough to allow the plasmon fieldto extend through it, maintaining plasmon-induced signal modification.By way of example only, the protective coating has a thicknessT_(Coating) of from about 1 nm to about 5 nm and ranges therebetween.See FIG. 16.

Exemplary methodologies for using the present graphene-based SPR sensorsfor analyzing a sample are now described by way of reference to FIGS.17-18 (transmission measurement) and 20 (reflection measurement). By wayof example only, the graphene nanoribbon configuration of the presentSPR sensor (of FIGS. 1-5) will be used in the figures to illustrate theimplementation process. However, the same process is performed in thesame manner with any of the SPR sensor configurations provided herein.

In general, the process will involve applying a sample to the surface ofthe present SPR sensor, which is subsequently illuminated with a certainspectral range of light. The plasmons in graphene excited by this lightinteract with the vibrational dipole moments in the sample in such a wayas to modulate (change) the output signal of the light transmittedthrough the sensor. This modulation can be constructive or destructive,is seen in the absorption spectrum of the outgoing light signal, andallows for sensitive identification of molecular compounds associatedwith chemical and/or biological species.

The details of the process are now provided. As shown in FIG. 17, thefirst step is to deposit a sample 1702 onto the present SPR sensor. Thesensor shown in FIG. 17 has the optional protective coating (i.e., inthis case coating 502) in place to protect the graphene during operationof the device. Specifically, as shown in FIG. 17, the sample isdeposited onto the graphene (i.e., in this case onto the nanoribbons302)—or alternatively onto the (optional) protective coating coveringthe graphene.

In one exemplary embodiment, the sample 1702 is a chemical and/orbiological material of interest. For instance, the present sensors maybe used to analyze biological samples including samples containinggenetic materials (such as DNA or RNA), proteins, enzymes, cell andtissue samples, etc. Chemical sensing and analysis using the presentsensors has a broad applicability to a wide variety of fields such aschemical compound and product testing, food analysis, drug analysis,etc. Advantageously, the present SPR sensors can be used to analyzesamples for which conventional analytics, such as IR spectroscopy wouldnot be able to detect because the sample is too small.

Generally, the analysis process using the present SPR sensors involvesusing incident light (provided by a light source) to cause excitation ofplasmons in the graphene. Interactions between the particular sample1702 and the graphene will affect the surface plasmon resonance of thegraphene. As a point of reference, a baseline spectrum is preferablyacquired without the graphene and sample (substrate). A spectrum withthe graphene and sample is then acquired. The final spectrum data canthen be given as a ratio between the sample+graphene+substrate spectrumand the substrate spectrum.

With that overall concept in mind, the next step is to provide a lightsource 1802 proximal to one side of the SPR sensor and the sample 1702and a detector 1804 proximal to an opposite side of the SPR sensor, suchthat light 1806 produced by the light source 1802 can pass through theSPR sensor and the sample 1702 to the detector 1804. See FIG. 18.Graphene is transparent to light, as are the conductive layer 104 a andthe insulating dielectric layer 104 b configured as described above.Thus, the light from the light source 1802 may easily pass through thesensor to the detector 1804. This configuration (i.e., light source anddetector on opposite sides of the sensor) assumes that the sensor useslight transparent materials. As described above, the back gate materialcan be intrinsic silicon which is transparent to light and can serve asan electrostatic gate electrode. Transmission measurements through thesensor may then be made.

On the other hand, if the gate electrode material used is a metal, thentransmission measurements are not possible since metals are nottransparent to light. In that case, reflection measurements can be madewhere the light source and the detector are located on the same side ofthe sensor proximal to the graphene. Incident light from the lightsource can be reflected off of the surface of the sensor at an angle andcaptured by the detector. This alternative configuration is shownillustrated in FIG. 20, described below.

One advantage of the present techniques is that surface plasmonresonance of the graphene is tunable by way of the patterning of thegraphene nanoribbons (as described above), and also by way of the chargedensity of the graphene. As such, the charge carrier concentration ingraphene is localized in such a way as to promote plasmon excitation. Byway of example only, as shown in FIG. 18, the charge density of thegraphene can be modulated using the field effect, e.g., by applying agate voltage 1808 to the conductive layer 104 a (which in this caseserves as a back gate electrode) to modulate the charge density of thegraphene. By modulating the charge density in the graphene, the plasmonresonance of the graphene can be shifted. For example, if a sample ofinterest has an intrinsic internal vibration at frequency A, but thegraphene plasmon resonates at frequency B, then the back gate can beused to change the charge density in the graphene and shift the plasmonresonance to overlap with frequency A. For p-doped (or n-doped)graphene, a more negative (or positive) gate bias will induce morecharge in the graphene, causing the plasmon resonance to shift to ahigher frequency. The more free charge in the graphene, the higher theplasmon frequency (for a constant nanoribbon width).

Another advantage of the present techniques is that prisms are notneeded to guide the incident light to the sensors. Specifically, inconventional designs, the angle of the incident light is important tocouple the incident light to the resonance of the plasmon material(commonly gold—see above). Without the correct angle, the desiredsurface plasmon resonance is not produced. Prisms are typically used todirect light at the proper angle to the sensor. While prisms aregenerally suited in that regard, they must be precisely implemented,which adds to device complexity and to overall production costs. Bycomparison, with the present SPR sensors, the angle of the incidentlight is not a factor, since coupling to the graphene can occur with thelight source 1802 at any position above the graphene surface of thedevice. Preferably, as shown in FIG. 18, the light source 1802 and thedetector 1804 are positioned in line with one another (based on the pathof the light 1806) with the SPR sensor centrally located therebetween.

Light 1806, generated by the light source, is then passed through thesample 1702 and the SPR sensor. See FIG. 18. As described above, theincident light 1806 on the sensor induces a plasmon resonance in thegraphene which is affected by the interaction of the sample 1802 and thegraphene. As a result, an intensity of the light 1806 exiting the sensor(and which is picked up by the detector 1804) is altered, e.g., ascompared to the light 1806 exiting the sensor when no sample is present.

According to an exemplary embodiment, a Fourier transform infraredspectroscopy setup (FTIR) is employed in conjunction with the presentSPR sensor wherein a broadband lamp is used as the light source 1802 ina Michelson interferometer with a movable mirror. Light from theinterferometer passes through the sample 1702 and the sensor to aninfrared detector (e.g., detector 1804), where the light signal isconverted to an electrical signal.

As shown in FIG. 18, a signal analyzer 1810 is used to analyze theelectrical signal from the detector 1804. As known in the art, a signalanalyzer is a device used to extract information from an electricalsignal. In this case, the data output from the signal analyzer is anabsorption spectrum. See FIG. 18. Suitable lightwave signal analyzersare commercially available, for example, from Agilent Technologies,Santa Clara, Calif. As highlighted above, the plasmon field generated inthe present SPR sensor interacts with dipole fields produced bymolecular vibrations in the chemical/biological material (i.e., sample1702) of interest. This interaction results in an absorption signalmodification that manifests itself as either an enhancement or reductionof the signal, and this change in the signal allows for more sensitivedetection of these molecular species. Specifically, graphene plasmonsand vibrational modes in the sample can interact either constructivelyor destructively with one another, giving either an increase or decreasein the light absorption signal (the IR absorption spectrum). By gatingthe sensor, as described above, the plasmon resonance frequency in thegraphene can be tuned for better coupling with the test species.

The analysis performed as illustrated in FIGS. 17 and 18 on the sample1702 can be used, for example, to analyze the molecular properties ofthe sample such as to detect the existence of a molecule in the sampleand also for molecular identification. It serves as a signal enhancementplatform for the infrared spectroscopy (e.g., FTIR). Thus, any sampleanalysis performed using IR spectroscopy can be performed in conjunctionwith the present techniques, however with a finer granularity andprecision due to the increased sensitivity afforded by the presentgraphene-based SPR sensor.

As described above, when patterned graphene nanoribbons are used in thepresent SPR sensors, the width of the nanoribbons is one factor thataffects, and thus can be used to control, the plasma resonance. FIG. 19is a diagram illustrating this effect in an exemplary case where theanalyte is a sample of PMMA. In FIG. 19, photon energy is plotted on thex-axis and absorption is plotted on the y-axis. As shown in FIG. 19, theabsorption spectrum shifts proportionally with the width of thenanoribbons (labeled “Ribbon width”).

As described above, transmission measurements require that thecomponents of the sensor are transparent to light. Thus whennon-transparent materials are used in the sensors (such as metals toform the back gate electrode), then alternate sensing methods areemployed, such as reflection measurements. The same analysis process asdescribed in conjunction with the description of FIGS. 17 and 18, above,is employed here, except that both the light source and the detector arelocated on the same side of the sensor. Thus, following from FIG. 17, asshown in FIG. 20, light 2006, generated by the light source 2002, isreflected off of the (graphene side) surface of the SPR sensor havingsample 1702 thereon onto the detector 2004. As described above, theincident light 2006 on the sensor induces a plasmon resonance in thegraphene which is affected by the interaction of the sample 1702 and thegraphene. As a result, an intensity of the light 2006 reflected off ofthe sensor (and which is picked up by the detector 2004) is altered,e.g., as compared to the light 2006 reflected from the sensor when nosample is present. As above, the charge density of the graphene can bemodulated using the field effect, e.g., by applying a gate voltage 2008to the conductive layer 104 a (which in this case serves as a back gateelectrode) to modulate the charge density of the graphene.

A signal analyzer 2010 is used to analyze the electrical signal from thedetector 2004. As highlighted above, the plasmon field generated in thepresent SPR sensor interacts with dipole fields produced by molecularvibrations in the chemical/biological material (i.e., sample 1702) ofinterest. This interaction results in an absorption signal modificationthat manifests itself as either an enhancement or reduction of thesignal, and this change in the signal allows for more sensitivedetection of these molecular species. By gating the sensor, the plasmonresonance frequency in the graphene can be tuned for better couplingwith the test species.

Although illustrative embodiments of the present invention have beendescribed herein, it is to be understood that the invention is notlimited to those precise embodiments, and that various other changes andmodifications may be made by one skilled in the art without departingfrom the scope of the invention.

What is claimed is:
 1. A method of forming a graphene-based SPR sensor,comprising the steps of: depositing a dielectric layer on a conductivelayer; patterning trenches at regular intervals in the dielectric layerto transform the dielectric layer into a corrugated surface having aseries of grooves and ridges, wherein the grooves are formed by thetrenches and the ridges are formed by the dielectric layer remainingbetween the trenches; and depositing bulk graphene onto the corrugatesurface of the dielectric layer, wherein the corrugated surface of thedielectric layer provides periodic regions of differing permittivitybeneath the bulk graphene comprising i) first regions having a firstpermittivity to light and ii) second regions having a secondpermittivity to light.
 2. The method of claim 1, wherein the trenchesare patterned so as to extend only partway through the dielectric layer.3. The method of claim 2, wherein a portion of the dielectric layerremaining at a bottom of the trenches has a thickness of at least about5 nanometers.
 4. The method of claim 2, wherein a portion of thedielectric layer remaining at a bottom of the trenches has a thicknessof from about 5 nanometers to about 20 nanometers and rangestherebetween.
 5. The method of claim 1, wherein each of the trenches hasa depth of from about 4 nanometers to about 300 nm and rangestherebetween.
 6. The method of claim 1, wherein the trenches arepatterned so as to extend completely through the dielectric layer, downto a surface of the conductive layer.
 7. The method of claim 1, whereinthe first regions having the first permittivity to light comprise theridges formed by the dielectric layer beneath the bulk graphene, andwherein the second regions having the second permittivity to lightcomprise air in the trenches beneath the bulk graphene.
 8. The method ofclaim 1, wherein the first regions having the first permittivity tolight comprise the ridges formed by the dielectric layer beneath thebulk graphene, and wherein the second regions having the secondpermittivity to light comprise a material in the trenches beneath thebulk graphene having a permittivity to light that is different from thedielectric layer.
 9. The method of claim 8, wherein the material havinga permittivity to light that is different from the dielectric layercomprises a different dielectric material from the dielectric layer. 10.The method of claim 8, wherein the dielectric layer comprises silicondioxide, and wherein the material in the trenches comprises a high-κdielectric.
 11. The method of claim 1, wherein the first regions areseparated from one another by a first distance that is measured from acenter of one of the first regions to a center of an adjacent firstregion, wherein the second regions are separated from one another by asecond distance that is measured from a center of one of the secondregions to a center of an adjacent second region, and wherein the firstdistance and the second distance are each from about 5 nanometers toabout 20 nanometers, and ranges therebetween.
 12. The method of claim 1,further comprising the step of: depositing a coating onto the bulkgraphene, wherein the coating comprises a transparent dielectricmaterial.
 13. The method of claim 12, wherein the coating has athickness of from about 1 nanometer to about 5 nanometers and rangestherebetween.
 14. The method of claim 1, wherein the dielectric layer isdeposited onto the conductive layer to a thickness of from about 4nanometers to about 300 nanometers and ranges therebetween.
 15. Themethod of claim 1, wherein the conductive layer comprises intrinsicsilicon.
 16. The method of claim 1, wherein the step of patterning thetrenches comprises the steps of: depositing a resist material onto thedielectric layer; patterning the resist material into an etch mask;etching the dielectric layer through the etch mask to transform thedielectric layer into the corrugated surface; and removing the etchmask.
 17. The method of claim 16, wherein the resist material comprisespolymethyl methacrylate (PMMA), and wherein the resist material ispatterned into the etch mask using e-beam lithography.
 18. The method ofclaim 1, wherein the bulk graphene comprises a graphene monolayer. 19.The method of claim 1, wherein the step of depositing the bulk graphenecomprises the steps of: growing the bulk graphene on a substrate; andtransferring the bulk graphene from the substrate to the corrugatesurface.
 20. The method of claim 1, further comprising the step of:doping the bulk graphene with an n-type or a p-type dopant.